One of the outstanding characteristics in the neural network operation is the use of nonlinear activation functions.
It is widely known that neural networks can establish efficient reduced order models thanks to the nonlinearity caused herein [1]}.
Wang et al. [2]} proposed a framework to predict the temporal evolution of proper orthogonal decomposition (POD) coefficients using the long short-term memory (LSTM) by considering an ocean gyre and a flow past a cylinder.
As an extension to turbulence, Srinivasan et al. [3]} used the LSTM to predict the temporal evolution of the coefficients of the nine equation model for a turbulent shear flow and reported its great potential.
Focusing on spatial order reduction, neural network-based low dimensionalization, i.e., autoencoder (AE), is also one of the promising candidates [4]}, [5]}.
The great role of nonlinear activation functions in neural networks was well summarized in Murata et al. [6]}, who compared AE-based modes to POD modes considering a laminar cylinder wake and its transient.
More recently, the customized AE referred to as a hierarchical AE was proposed by Fukami et al. [7]} to handle turbulent flows efficiently.
